Where L is the angular momentum. This equation tells us we can multiply a linear momentum by a radius and achieve an angular momentum. Is that sensible? No. It implies a big problem of scaling, for example. If r is greater than 1, the effective angular velocity is greater than the effective linear velocity. If r is less than 1, the effective angular velocity is less than the effective linear velocity. How is that logical?

Utter nonsense. Regardless of the value of r, angular velocity and linear velocity are measured in different units, so it's an apples-and-oranges comparison from the get-go. Whether an object's angular velocity is numerically greater or less than its linear velocity is a consequence of your choice of units and has no significance beyond that.

Hi Painterman,

I do not believe that you either understood or read consistently that paper from the link above.

Using nothing more than pure logic : current MSM formulas for linear and angular momentum imply exactly what Mathis has pointed to -> being a mix of apples and oranges. Yet the logic you applied to the written paper by MM and that of the MSM theory is twice mistaken.

Whether an object's angular velocity is (numerically) greater or smaller than its linear velocity is NOT a consequence of anyone's choice it is a matter of physics laws and thus mechanics is involved. It represents a fact, regardless of what humanoids wish to choose, and this fact should be represented in a formula, which should allow for the correct calculation and units of the result.

What Mathis logically concluded from the above MSM (!) formulas (p=mv; L=rmv) is consistent with reality - in two ways : it is not compliant in relation to the involved units (when we go from linear to angular momentum and vice versa) and it is not logical at all when radius (r) gets smaller than 1. Think about the latter as it implies logical error which is just absurd. Maybe I demand to much from you regarding it, however if it should be to much for you to understand its absurdity as-is , maybe you should avoid writing about it in demonstrated manner. Utter nonsense could be thrown back at you, easily, but with what intention? What could I possibly achieve with such an act?

What you properly showed, nevertheless, is the need to correct existing momentum equations not to be a mix of apples and oranges anymore. Could it be that Mathis is on top of it?

Also, the document text has a bit of his history with those mainstream charlatans.

Call me clueless, but . . .

Since Pi is defined as "The ratio of a circle's circumference to its diameter," how does adding any variable not included in the definition (e.g., velocity) have anything to do with the essential definition? (Rolling a ball along a straight path and another ball along a curved path at the same initial velocity will yield different time per distance traveled at the end of the measurement. So, what's that got to do with pi, the geometric constant?)

Since Pi is "The ratio of a circle's circumference to its diameter," how does adding any variable not included in the definition (e.g., velocity) have anything to do with the essential definition? (Rolling a ball along a straight path and another ball along a curved path at the same initial velocity will yield different time per distance traveled at the end of the measurement. So, what's that got to do with pi, the geometric constant?)

Here is an excerpt from the paper that DSKlausler linked to:

Some have taken exception to my way of stating that. They say that pi is 3.14... and can't also be 4.They say I should come up with another Greek letter, at the least. But pi isn't defined as 3.14. Pi isdefined as the ratio of the circumference and the diameter. I have proved that when motion is involved,that ratio is 4. Therefore, it is correct to say that pi=4.

Others have said that even if I am right, it is just a quibble, since in most cases pi will still be 3.14. Butthat simply isn't true. In physics—and therefore in the real-world—almost all uses of pi includemotion. When pi is used in physical equations, 99% of the time those equations include a velocity ofsome sort.

Whenever I have posted in other forums about Miles's physics work, somebody always appears to discredit him saying "this is the guy that believes Pi=4." I personally think Miles shot himself in the foot by stating his claim in this way. I think it also adds confusion. The choice of Greek letter to represent a mathematical constant is fairly arbitrary. But once it's chosen, it won't do to say that actually that constant is a different number. It even more won't do to say it is different numbers depending on the situation. And in fact Miles is arguing that Pi=4 in some situations. So that only add to the confusion, because we usually think of mathematical constants as constant, so in a sense he is telling us that it's not constant but depends on the situation in which it's used.

I personally think he would have been better off choosing a different greek letter and making his argument something like: in situations X, we need to use Pi (=3.14) to calculate the circumference, but in other situations, we need to use (i don't know) Omicron (=4) to calculate the circumference. But Miles says he did it deliberately to be provocative, and he certainly succeeded in that.

But even then the whole business is confusing. One way to think about it: it takes more time to move in a circular path than in a straight line. When you're moving around a circle, it takes the same amount of time to travel 3.14 units of measurement as it does to travel to 4 units in a straight line. Another way of thinking about it is that anything moving in the circular path will necessarily take 4 times as a long as a linear motion across 1 diameter (whereas we would normally think it would take 3.14 times as long). The crucial point here is that it has nothing to do with velocity. The movement takes place at the same speed, as it were. It's not due to slowing down around the curve. This latter point is crucial and is what makes it so mind-boggling.

The reason is that the distance around a curve is longer. Miles differentiates between length and distance: "A length is a given parameter that does not include motion or time. It is geometric only. But a distance is a length traveled in some real time, so it requires motion. A length is not kinematic, while a distance is." So if you're talking about lengths (such as those measured by a tape measure), Pi=3.14. When you're talking about distance (as he defines it), then Pi (or Omicron) = 4.

If you watch the video, what is not immediately obvious is that the length of the circular tube is the exact same length as the 'Pi' marking on the straight tube (you can do the calculations from the measurements given at the end). So if you straightened the tube, the balls would arrive at the 'Pi' marking at the same time, which for the shorter tube would be the end. Then if you bend it back into a circle, you'd see that the ball reaches the end of the circular tube at the same time as the ball in the straight tube reaches the 4 mark at the end -- even though both balls are travelling at the same speed. And yet, if you measure it out and divide the length of the circular tube by its diameter, you'll get good ol' Pi=3.14. I don't know about you, but to me that's just bonkers.

Now, I would agree with criticism stating that we need better documentation/proof that the speed really doesn't change, although the video does offer a fair amount. Apparently Steve Oostdijk (who did the experiment and has been accused of being one of Miles's aliases/sock puppets) is going to redo the experiment to offer more evidence of this. I believe he will be vindicated.

I would also like to point out that this astonishing result ultimately arises from of one of Miles's key postulates or working assumptions, which is that there are no zeros or points in physics. Everything that exists must have physical extension. That being so, physical objects cannot be represented mathematically by a point or a zero or an infinitesimally small length. So you have to be careful when applying math and geometry to physical equations. Here I'll just quote from http://milesmathis.com/central.html:

That oldest mistake is one that Euclid made. It concerns the definition of the point. Entire library shelves have been filled commenting on Euclid's definitions, but neither he nor anyone since has appeared to notice the gaping hole in that definition. Euclid declined to inform us whether his point was a real point or a diagrammed point. Most will say that it is a geometric point, and that a geometric point is either both real and diagrammed or it is neither. But all the arguments in that line have been philosophical misdirection. The problem that has to be solved mathematically concerns the dimensions created by the definition. That is, Euclid's hole is not a philosophical or metaphysical one, it is a mechanical and mathematical one. Geometry is mathematics, and mathematics concerns numbers. So the operational question is, can you assign a number to a point, and if you do, what mathematical outcome must there be to that assignment? I have exhaustively shown that you cannot assign a counting number to a real point. A real point is dimensionless; it therefore has no extension in any direction. You can apply an ordinal number to it, but you cannot assign a cardinal number to it. Since mathematics and physics concern cardinal or counting numbers, the point cannot enter their equations.

This is of fundamental contemporary importance, since it means that the point cannot enter calculus equations. It also cannot exit calculus equations. Meaning that you cannot find points as the solutions to any differential or integral problems. There is simply no such thing as a solution at an instant or a point, including a solution that claims to be a velocity, a time, a distance, or an acceleration. Whenever mathematics is applied to physics, the point is not a possible solution or a possible question or axiom. It is not part of the math.

Now, it is true that diagrammed points may be used in mathematics and physics. You can easily assign a number to a diagrammed point. Descartes gave us a very useful graph to use when diagramming them. But these diagrammed points are not physical points and cannot stand for physical points. A physical point has no dimensions, by definition. A diagrammed point must have at least one dimension. In a Cartesian graph, a diagrammed point has two dimensions: it has an x-dimension and a y-dimension. What people have not remembered is that if you enter a series of equations with a certain number of dimensions, you must exit that series of equations with the same number of dimensions. If you assign a variable to a parameter, then that variable must have at least one dimension. It must have at least one dimension because you intend to assign a number to it. That is what a variable is—a potential number. This means that all your variables and all your solutions must have at least one dimension at all times. If they didn't, you couldn't assign numbers to them.

This critical finding of mine has thousands of implications in physics...

HonestlyNow » September 26th, 2016, 10:49 pm wrote:Since Pi is defined as "The ratio of a circle's circumference to its diameter," how does adding any variable not included in the definition (e.g., velocity) have anything to do with the essential definition? (Rolling a ball along a straight path and another ball along a curved path at the same initial velocity will yield different time per distance traveled at the end of the measurement. So, what's that got to do with pi, the geometric constant?)

Miles does not dispute the fact that in geometry circumference of the circle is the defined as ratio to its diameter, which we know as Pi and its "constant" value of 3,14etc . So visualization of this particular issue is very important, because when we have movement involved, "standard" Euclidean formulation of the above mentioned ration just doesn't work out to be as observed in the physical reality. While at motion, the value of circumference of the circle does not equal the length of physical path of any point on circle's boundary (at R distance from its center) , which is the essence of this thesis/theory. As he says here:

If you roll a wheel on the ground one full rotation, it will mark off a path on the ground that is 2πr in length, as most people know. That length has been assigned to the circumference of the circle or wheel, which assignment is correct as far as it goes. My papers have not questioned that. However, if you do the same thing but follow the motion of a given point on the wheel (point A in the diagram above, for instance), it draws the red curve. That is called the cycloid. Obviously, the red curve is not the same length as the line on the ground. It is considerably longer, being 8r in length. That is 21% longer than the circumference.

full link to his paper :http://milesmathis.com/cycloid.pdf

The video about the experiment showing this discrepancy is just a "real time animation" which is to replace rolling a wheel on the ground one full rotation. Purpose of it is to show that while in motion, the ball covers actually 8R of lenght of a certain circle (curve) , and not 2πR of its lenght. And this is where 21% of error shows up each time you try to apply the static, Euclidean version of understanding the Pi to actual physics being observed, even at most simple of experiments.

(Edit: As daddie_o correctly applied : lenght and distance are very important to be used correctly. Thus I should replace all my applied "lenght" with correct "distance", just to be consistent with the point being made here.)

daddie_o wrote:[...] physical objects cannot be represented mathematically by a point or a zero or an infinitesimally small length. So you have to be careful when applying math and geometry to physical equations.

I read Miles' paper cursorily but was not enlightened. I am not sure whether it´s mind-boggling or just confusing. I think I need to give it another try.

The argument that zero (or an abstract point) cannot be the beginning of the series of cardinal numbers or of spatial extension was conclusively demonstrated by René Guénon in Chapter 15 of The Metaphysical Principles of the Infinitesimal Calculus (1946).

A word or a character is used as a symbol in language to express a communicator's concept. The symbol known as "pi" is used to express the concept of "The ratio of a circle's circumference to its diameter." Nothing in that definition includes the concept denoting that velocity is a part of that definition — it is strictly a geometric concept. By changing an aspect of the concept, in order to communicate in a more effective manner, one would need to use a different symbol, and the parties privy to this conversation would need to come to terms as to the meaning of this up-until-now unfamiliar symbol.

That 'CYCLOID' paper by MM contains some quite interesting musings (of 'general nature') - which I'd just like to highlight for future reference :

MilesMathis wrote:So it is a bit strange that doing the same thing—rolling the wheel one rotation—gives us two verydifferent path lengths. Both of them are physical and real. Neither seems to be abstract or mystical inany way. But for some reason the cycloid has been pretty much ignored in the history of physics. It isused in the problem of the rolling wheel and nowhere else. It isn't used for anything important, beingcompletely overshadowed by the circumference and by π.

My feeling is that this is due to the problem most people have with visualizing math—or anything elsefor that matter. I have found by long experience that most people aren't very visual. If you are veryvisual, you tend to go into art or design, not into science. In fact, scientists and mathematicians aregenerally the least visual people I know. That is a strange circumstance, and I don't think it is anecessary outcome of history or science, but currently that is the way it is. It has a lot to do with thepolitics of science and physics in the 20th century, and with the specific people that were involved in it.

Well, I have a pretty strong hunch as to why exactly, as MM muses, "the cycloid has been pretty much ignored in the history of physics". As it happens, one of the main findings of my ongoing cosmic research has to do with so-called prolate cycloid motion. I won't / can't say more for now (and sorry for sounding 'cryptic') other than that, according to my upcoming cosmic model, ALL OF US earthlings physically perform a full cycloid each year - and due to this hitherto unknown (or wilfully 'occulted'?) annual terrestrial motion - affecting ALL earthly observers - astronomers have continuously reached erroneous conclusions as to the celestial mechanics of our surrounding planets and stars (and of Earth itself - of course). Again, I apologize for the 'teasing vibe' of this brief post of mine - but there's just no way I can elaborate on this at this stage, in any succint / easily-comprehensible manner. Also, sorry all - for being so slow to publish my model : a series of rather harrowing / time-consuming daily-life circumstances keep delaying the completion of my thesis. Hopefully, I should soon get back to normal work pace - and release my model within the year.

I went around and around with this Pi business. Eventually I decided it's correct and based on some very deep insights. A better and more thorough paper to read, I think, is this one: http://milesmathis.com/pi2.html

As for the confusion, I'll just quote this passage from the paper I linked to:

...this paper cannot stand alone. It is a mistake to start with this paper. Those who do start with this paper will very likely be led to believe I am simply doing the calculus wrong. To these people, I say that it is not I who am doing the calculus wrong. It is Newton and Leibniz and Cauchy and everyone since who has been doing the calculus wrong. I have earned the right to write this paper by first writing three important papers on the foundations of the calculus. The first shows that the derivative has been defined wrongly from the beginning, and that the derivative is a constant differential over a subinterval, not a diminishing differential as we approach zero. There is no necessary approach to zero in the calculus, and the interval of the derivative is a real interval. In any particular problem, you can find the time that passes during the derivative, so nothing in the calculus is instantaneous, either. This revolutionizes QED by forbidding the point particle and bypassing all need for renormalization. The second paper proves that Newton's first eight lemmae or assumptions in the Principia are all false. Newton monitors the wrong angle in his triangle as he goes to the limit, achieving faulty conclusions about his angles, and about the value of the tangent and arc at the limit. Finally, the third paper rigorously analyzes all the historical proofs of the orbital equation a=v2/r, including the proofs of Newton and Feynman, showing they all contain fundamental errors. The current equation is shown to be false, and the equation for the orbital velocity v=2πr/t is also shown to be false. Those who don't find enough rigor or math in this paper should read those three papers before they decide this is all too big a leap. I cannot rederive all my proofs in each paper, or restate all my arguments, so I am afraid more reading is due for those who really wish to be convinced. This paper cannot stand without the historical rewrite contained in those papers, and I would be the first to admit it.

Well, interesting posts on the subject...quite some thoughts about it.

Honestlyknow, you are absolutely right :

By changing an aspect of the concept, in order to communicate in a more effective manner, one would need to use a different symbol, and the parties privy to this conversation would need to come to terms as to the meaning of this up-until-now unfamiliar symbol.

Pi is a known constant of geometry. There is only one thing though to think about, since majority of all applications of this particular constant involves motion , we should consider making "fundamental" Pi as value of 4 and consequently re-name the constant used in geometrical applications. But definitely, we need 2 separate simbols/latin letters/whatever to mark 2 separate definitions/concepts and avoid misunderstanding.

Not to get the focus redirected, what you were arguing against primarily is not in connection to naming / using the symbol properly, it was about the ratio (of circle's diameter to its circumference). When applying standard value of 3,14..., it fails to describe mechanically what is observed. If instead we use for Pi value of 4, the ratio is correctly described. It happens while a perfect circle is in motion describing one full cycle, so the cycloid geometry is what we are focusing on. Still, it is not just us who would argue on naming a constant (ratio) properly, all of those who would try to describe the physics/mechanics of such motion would enter into it, since proper symbols need to be applied to express thoughts correctly and consistently. So, semantically, you are completely right - we should use different name/symbol for kinematic ratio. However, the point is still made (though rather dramatically by Miles who purposely used established Pi in kinematic situation to make some attention to himself) and this ratio of hyperfamous Pi was not supposed to be in question ever, that's what the word "constant" means. True or not? But it looks as if we were all blind to the fact of cycloid and the logic it implies, it's just unbelievable.

Simon, I really can't wait to see what you are talking about . I bet it will be interesting though ....

Flabbergasted, I hope you didn't enter into Mathis' theory with THAT subject . That would REALLY be mind-boggling

Interesting: 8 years after he posted his paper on pi, you can see a simple experiment that apparently verifies his conclusions (pi=4 when motion is involved) that you can replicate.

His arguments in the accompanying article give credibility to both the American and Russian space programs and to quantum mechanics. As usual he doesn't give any sources, which bothers me.

In the late,1950s, the American program headed by Werner von Braun began admitting major equation failures....The Russians found the same problem. ....A similar problem arose in quantum mechanics. Since quantum particles often move in orbits or curved trajectories, the same sort of equation failures occurred there. The mainstream admits it has to ditch classical geometry and resort to what is called the Manhattan metric to solve some quantum problems. This is curious since in the Manhattan metric pi=4*.

Are there no examples to be found in other fields, that we can actually verify? Do you know of any, Vexman? You wrote "since majority of all applications of this particular constant involves motion", so you are actually saying the majority of applications of pi give wrong results.

*By the way, it seems to me that the only reason pi=4 in the Mahattan metric is because their circles are actually squares. So they are just saying pi=4 for squares (and circles are squares as Hoi wrote rather sarcastically at the start of this topic) Is this not a different reason then Mathis' ?

Seneca, sure, I can count a few examples of kinematic circular motion in real life : an archer shooting his arrow, playing a ball/badminton game with my children, jumping into the sea for a swim, catching a friends lighter thrown at me, trying to save a glass from smashing while falling from my desk,....I claim that in all named cases, trying to mathematically prove trajectory would bring wrong results by 21% if Pi=3,14... is used to calculate their location (as opposed to where you'd actually find them). Considering all being written here and by Mathis himself, it makes sense. It is true though that common sense is not so common after all. Now, can you kindly provide me with some examples of applications of Pi without (!) motion involved? (i.e. to draw a central circle in the soccer field is not en example)

Another fact is that I never actually tried to confirm value of Pi in my life so far (except while at school's exams in geometry), so I really might do it just for my own entertainment. However, to think of an experiment and to execute one in order to prove (or dismiss) a thesis in physics is admirable act done by anyone. Even more so if it is an elegantly simple thing to prove a groundbreaking thesis. So it is interesting indeed, that a Dutchman in the video got motivated and tried to manifest what we're arguing here. I believe I can understand him perfectly, he was troubled by the Pi thing as many other of us. When I find time I will most certainly follow in his example. Until then, I'll just use my belief system to rationalize it, just as I did with the until-recent constant of 3,14...

True, Mathis sometimes lacks some footnotes to link them to his claims. I do/did notice it, however in his science work it can be usually confirmed already at WikiLand. I.e. :

Von Braun's insistence on further tests after Mercury-Redstone 2 flew higher than planned has been identified as contributing to the Soviet Union's success in launching the first human in space.

(from here : https://en.wikipedia.org/wiki/Wernher_von_Braun#American_career ). It doesn't confirm Mathis' claims, it does though indicate that although tens or even hundreds of top NASA scientists were working and calculating all possible things, the rocket did surprise them and flew higher... How truly surprising

Now, can you kindly provide me with some examples of applications of Pi without (!) motion involved?

You might want to figure out the footprint, volume, density, circumference or other characteristics of a round or semi-circular object. Moving things, filling space with liquids, even decorating, etc. Sorry, but even when Miles' revolution comes and all the academics jump from their text books, I don't think pi is going extinct.

Discovering a new formula is a pretty cool discovery, though! Has it been written yet in traditional latin-type characters, for the eggheads to use?

Discovering a new formula is a pretty cool discovery, though! Has it been written yet in traditional latin-type characters, for the eggheads to use?

Pi will never be abolished as a constant, no one can refute it in geometry and static situations. It's more like Honestlyknow said, we should introduce another symbol to be used as ratio=4 in kinematic situations to avoid misunderstanding and develop an expression/terminology for such use. I think that would be enough for starters, since acknowledging it as a definition seems like a heresy, something outrageous.

No progress here yet, it would be an interesting bet to make - when (if at all) could we expect physics as is to change its definition regarding kinematic circular motion? I sure hope to see it before I die Until then I guess you and I will be marked as cranks, followers of that hypercrank guy who claims Pi=4

Vexman, thanks for finding that in Wikipedia. It is not exactly what Mathis wrote but it goes in the same direction. But for all I know Werner Von Braun could be just an actor in a movie.That is why I asked if there are no examples to be found in other fields, that we can actually verify. I meant examples were the use of pi when motion is involved gives wrong results and this is noticed by real scientists or real people.

Mathis and his followers had 8 years to find these examples and the only ones I have seen mentioned are the ones I quoted in my earlier post.If I understand correctly the effect should be noticed in athletics. Running the same length on a circular/oval track should take longer than running in a straight line at the same speed.It should also be noticed in the use of route planners. Trajectories with lots of curves should take longer than is calculated when this is not taken into consideration. Actually in my experience, the time travelled in reality is often indeed longer than the time calculated by route planners like Google maps.